giving an action of the cyclic group of order 3. This can be made to look more symmetrical by regarding the original two-variable adjunction as a “two-variable left adjunction” C×D→EopC\times D \to E^{op}; see Cheng-Gurski-Riehl.

Adjunctions of nn variables

There is a straightforward generalization to an adjunction of nn variables, which involves n+1n+1 categories and n+1n+1 functors. Adjunctions of nn variables assemble into a 2-multicategory. They also have a corresponding notion of mates; see Cheng-Gurski-Riehl.